note explains the following topics: Symplectic geometry, Fourier transform,
stationary phase, Quantization of symbols, Semiclassical defect measures,
Eigenvalues and eigenfunctions, Exponential estimates for eigenfunctions,
symbol calculus, Quantum ergodicity and Quantizing symplectic
This note explains the following topics:
linearly related sequences of difference derivatives of discrete orthogonal
polynomials, identity for zeros of Bessel functions, Close-to-convexity of
some special functions and their derivatives, Monotonicity properties of
some Dini functions, Classification of Systems of Linear Second-Order
Ordinary Differential Equations, functions of Hausdorff moment sequences,
Van der Corput inequalities for Bessel functions.
seven chapters of this monograph discuss the techniques involved in symbolic
calculus have their origins in symplectic geometry. Remaining chapters
explains wave and heat trace formulas for globally defined semi classical differential operators on manifolds and
equivariant versions of these results involving Lie group actions.